Step |
Hyp |
Ref |
Expression |
1 |
|
kqval.2 |
|
2 |
|
regr1lem.2 |
|
3 |
|
regr1lem.3 |
|
4 |
|
regr1lem.4 |
|
5 |
|
regr1lem.5 |
|
6 |
|
regr1lem.6 |
|
7 |
|
regr1lem.7 |
|
8 |
3
|
adantr |
|
9 |
6
|
adantr |
|
10 |
|
simpr |
|
11 |
|
regsep |
|
12 |
8 9 10 11
|
syl3anc |
|
13 |
7
|
ad2antrr |
|
14 |
2
|
ad3antrrr |
|
15 |
|
simplrl |
|
16 |
1
|
kqopn |
|
17 |
14 15 16
|
syl2anc |
|
18 |
|
toponuni |
|
19 |
14 18
|
syl |
|
20 |
19
|
difeq1d |
|
21 |
|
topontop |
|
22 |
14 21
|
syl |
|
23 |
|
elssuni |
|
24 |
15 23
|
syl |
|
25 |
|
eqid |
|
26 |
25
|
clscld |
|
27 |
22 24 26
|
syl2anc |
|
28 |
25
|
cldopn |
|
29 |
27 28
|
syl |
|
30 |
20 29
|
eqeltrd |
|
31 |
1
|
kqopn |
|
32 |
14 30 31
|
syl2anc |
|
33 |
|
simprrl |
|
34 |
33
|
adantr |
|
35 |
4
|
ad3antrrr |
|
36 |
1
|
kqfvima |
|
37 |
14 15 35 36
|
syl3anc |
|
38 |
34 37
|
mpbid |
|
39 |
5
|
ad3antrrr |
|
40 |
|
simprrr |
|
41 |
40
|
sseld |
|
42 |
41
|
con3dimp |
|
43 |
39 42
|
eldifd |
|
44 |
1
|
kqfvima |
|
45 |
14 30 39 44
|
syl3anc |
|
46 |
43 45
|
mpbid |
|
47 |
25
|
sscls |
|
48 |
22 24 47
|
syl2anc |
|
49 |
48
|
sscond |
|
50 |
|
imass2 |
|
51 |
|
sslin |
|
52 |
49 50 51
|
3syl |
|
53 |
1
|
kqdisj |
|
54 |
14 15 53
|
syl2anc |
|
55 |
|
sseq0 |
|
56 |
52 54 55
|
syl2anc |
|
57 |
|
eleq2 |
|
58 |
|
ineq1 |
|
59 |
58
|
eqeq1d |
|
60 |
57 59
|
3anbi13d |
|
61 |
|
eleq2 |
|
62 |
|
ineq2 |
|
63 |
62
|
eqeq1d |
|
64 |
61 63
|
3anbi23d |
|
65 |
60 64
|
rspc2ev |
|
66 |
17 32 38 46 56 65
|
syl113anc |
|
67 |
66
|
ex |
|
68 |
13 67
|
mt3d |
|
69 |
12 68
|
rexlimddv |
|
70 |
69
|
ex |
|